There are 10 cups placed on a table such that 3 are face up and 7 are bottom up. A move is defined as inverting a pair (compulsorily) of cups. What is the minimum number of moves required to make all the cups face the same way?
64 numbers (not necessarily distinct) are placed on the squares of a chessboard such that the sum of the numbers in every 2x2 square is 7.
What is the sum of the four numbers in the corners of the board?
A circular cone with height 24 and radius 6 is placed on its circular face on a table. It is then cut by a horizontal plane, which is parallel to the circular base and passes through the midpoint of the height. The volume of the lower part of the cone can be written as A*PI.
What is the value of A?
There are 100 coins placed on a table in a dark room, out of which 20 coins are showing tails and 80 coins are showing heads. The task is to divide this set of 100 coins into 2 groups (not necessarily same size) such that both groups have the same number of coins showing the tails.
Below is a multiplication table up to y*y. Find y such that the sum of all the products in the table equals 44488900?
